The present invention relates to frequency domain Least Mean Square (LMS) filters, and more particularly, to an LMS filter whose operation is normalized in each frequency bin by the spectral power in that bin, thereby providing stable filter operation in each frequency bin even for an input signal having differing signal powers in each frequency bin.
The time-domain LMS adaptive filter algorithm has found may applications in situations where the statistics of the input processes are unknown or changing. These include noise cancellation, line enhancing, and adaptive array processing. The algorithm uses a transversal filter structure driven by a primary input, so as to minimize the mean-square error of the difference.
In general, the stability, convergence time, and fluctuations of the adaptation process are governed by the product of the feedback coefficient .mu. and the input power to the adaptive filter. As a result, in practical applications, there is an implicit automatic gain control (AGC) on the input to the adaptive filter. The AGC ensures that the .mu.-power product is maintained within acceptable design limits. When the adaptive filter is implemented as a tapped delay line operating on the entire available input signal bandwidth, selection of a single value .mu. is required. Then, the algorithm convergence time and stability depends upon the ratio of the largest to the smallest eigenvalues associated with the correlation matrix of the input sequence. The smaller the ratio, the better the convergence and misadjustment noise properties of the algorithm.
More recently, the computational efficiencies resulting from processing blocks of data, such as the fast Fourier transform (FFT) and block digital filtering, has led to the implementation of the LMS adaptive algorithm in the frequency domain. The primary and reference channels are both transformed, and an adaptive weight is placed between them on each frequency bin. The LMS algorithm reduces to a single complex weight and the feedback sequence of errors is just the error computed in each bin.
In addition to the computational advantages of the frequency domain adaptive filter (FDAF), significant analytical advantages, compared to the time domain LMS adaptive filter, occur when using the FDAF, e.g., for determining first and second-moment properties of the FDAF complex weights, and under certain mild conditions, for predicting the performance of the time domain LMS adaptive filter.
When evaluating the performance of the FDAF, it is still implicitly assumed that some sort of gain control exists so that the feedback coefficient .mu. on each complex weight update, can be selected for a known input power. If the input waveform is spectrally flat over the band, then the same broad-band AGC used in the tapped delay line implementation will suffice for each frequency bin. In most practical cases, this is how the frequency domain adaptive filter is configured.
The non-spectrally flat case for which the powers in each bin differ (perhaps dramatically) presents a problem. In some applications, where rapid convergence is necessary and a single .mu. is used based on the broad-band power level, the increase in spectral level in some bins may cause instability in the adaptive weights at those frequencies. This corresponds to the time-domain case where the ratio of the largest to smallest eigenvalue of the data covariance matrix is very large.
There is therefore a need for a frequency domain LMS filter which provides stable operation for non-spectrally flat input signals.